Ratios of Circumference

[2partswater]

I'm so lost and cannot find this information anywhere in my online lessons. Here is the question:

One circle has a radius of 1/4 and another circle has a radius of 2. What is the ratio of the circumference of the larger circle to the circumference of the smaller circle?

So, if C = PI(r-squared), then for the first circle, it would be C = 3.14(1/4^2) = .19625 and for the second, C = 3.14(2^2) = 12.56 but do I even need to do that? The circumferences would be 1/2 and 4 so would be answer be 1:8 or 1:64?

 

[Quaid]

I'm so lost and cannot find this information anywhere in my online lessons.

These are common laments, from students taking on-line courses.

One circle has a radius of 1/4 and another circle has a radius of 2. What is the ratio of the circumference of the larger circle to the circumference of the smaller circle?

Let C = the larger circumference

Let c = the smaller circumference

The statement, "ratio of the larger to the smaller" tells us that C comes before c in each form of the ratio statement

C to c

C:c

C/c

So, if C = PI(r-squared)

Oops! That's not the formula for circumference.

Circumference = 2 * Pi * r

Area = Pi * r^2

Let us know, if you need more help writing the answer. Please show your work.

Cheers

PS: Here's a link to the summary page of the forum guidelines.

 

[2partswater]

Oh my god. Duh. Thank you!

 

[HallsofIvy]

"Circumfernce" and "radius" are both linear measurements so are in the same ratio. If one circle has radius $\displaystyle \frac{\frac{1}{4}}{2}= \frac{1}{8}$ as large as the other, then the circumferences are in the same ratio.